aba : assumption-based argumentation with preferences · argumentation with preferences ways to...

ABA+: Assumption-Based Argumentation withPreferences

Cardiff Argumentation Forum

Kristijonas Cyras Francesca Toni

Imperial College London

July 7, 2016

Kristijonas Cyras

ABA+: Assumption-Based Argumentation with Preferences

Argumentation with Preferences

Ways to account for preferences:

I Encode within existing components

I Discard attacks

I Compare extensions

Kristijonas Cyras


1. Encode preferences within existing components

I Preferences as assumptions [Kowalski and Toni, 1996]

I (Sets of) sentences into assumptions and rules[Thang and Luong, 2014]

Issues:I concision

I modularity

I generalizability

Kristijonas Cyras


2. Discard attacks

Given (Args, ,6): if A B and A < B, then A 6 B.

I Abstract Argumentation[Amgoud and Cayrol, 2002, Bench-Capon, 2003,

Kaci and van der Torre, 2008]

I Structured argumentation[Prakken and Sartor, 1999, Besnard and Hunter, 2014,

Garcıa and Simari, 2014, Modgil and Prakken, 2014]

Issues:I conflict-freeness

I restrictions

Kristijonas Cyras


3. Compare extensions

Lift preferences to the extension level from:I the argument level [Amgoud and Vesic, 2011] (AA);

I the object level [Wakaki, 2014] (ABA).

Issues:I absence of extensions

I ‘wrong’ extensions

I preference aggregation

Kristijonas Cyras


Omissions

I *Encode within/discard attacks [Modgil, 2009,Baroni et al., 2011, Brewka and Woltran, 2010]

I Bipolar Argumentation Frameworks [Amgoud et al., 2004]

I [Villata et al., 2012]: AA with prioritized support

I [Dunne et al., 2011]: weighted attacks, inconsistencybudget

I [Booth et al., 2013]: arguments with properties,motivational states, weighting relation

Kristijonas Cyras


Attack Reversal in Abstract Argumentation

Proposed for AA: (Rich) PAFs [Amgoud and Vesic, 2014].

Given (Args, ,6): if A B and A < B,then A 6↪→ B and B ↪→ A.

Example

Args = {A,B}, A < B:

(Args, ,6)

A B

(Args, ↪→)

A B

Kristijonas Cyras


Attack Reversal in Structured Argumentation

I Assumption-Based Argumentation (ABA)[Bondarenko et al., 1997, Dung et al., 2009, Toni, 2014]

I ABA+ [Cyras and Toni, 2016a, Cyras and Toni, 2016b]:ABA with preferences over assumptions

Kristijonas Cyras


ABA

I ABA framework (L,R,A, ¯):I deductive system (L,R);I assumptions A ⊆ L;I contrary mapping ¯ : A → L.

I Tree-like deductions S `R ϕI Attacks as deductions for contraries

I Semantics: extensions as sets of assumptions

Kristijonas Cyras


ABA+

I ABA+ framework (L,R,A, ¯ ,6):I ABA framework (L,R,A, ¯);I transitive binary 6 on A.

I New attack relation <:I if A B (‘on β ∈ B’) and no α ∈ A with α < β,

then A < B;I if A B (‘on β ∈ B’) and some α ∈ A has α < β,

then B < A.

Kristijonas Cyras


ABA vs. ABA+

Formally

I A ⊆ A

<-

attacks B ⊆ A just in case:

I either

A′ `R β, for some β ∈ B and A′ ⊆ A,

and ∀α′ ∈ A′ we have α′ 6< β;

I or B ′ `R′α, for some α ∈ A and B ′ ⊆ B ,

and ∃β′ ∈ B ′ with β′ < α.

Kristijonas Cyras


ABA vs. ABA+

Formally

I A ⊆ A <-attacks B ⊆ A just in case:I either A′ `R β, for some β ∈ B and A′ ⊆ A,

and ∀α′ ∈ A′ we have α′ 6< β;

I or B ′ `R′α, for some α ∈ A and B ′ ⊆ B ,

and ∃β′ ∈ B ′ with β′ < α.

Kristijonas Cyras


ABA vs. ABA+

Formally

I A ⊆ A <-attacks B ⊆ A just in case:I either A′ `R β, for some β ∈ B and A′ ⊆ A,

and ∀α′ ∈ A′ we have α′ 6< β;I or B ′ `R′

α, for some α ∈ A and B ′ ⊆ B ,and ∃β′ ∈ B ′ with β′ < α.

Kristijonas Cyras


Simple Example

L = {α, β, α, β}, R = {β ← α}, A = {α, β}

, α < β.

ABA

∅ {α} {β} {α, β}

ABA+

∅ {α} {β} {α, β}reverse

Kristijonas Cyras


Simple Example

L = {α, β, α, β}, R = {β ← α}, A = {α, β} , α < β.

ABA

∅ {α} {β} {α, β}

ABA+

∅ {α} {β} {α, β}reverse

Kristijonas Cyras


Cycle

R = {β ← α; γ ← β; α← γ}, A = {α, β, γ},

γ < β < α.

ABA

{γ}{β}

{α}

ABA+

{γ}{β}

{α}normal

reverse

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Cycle

R = {β ← α; γ ← β; α← γ}, A = {α, β, γ}, γ < β < α.

ABA

{γ}{β}

{α} ABA+

{γ}{β}

{α}normal

reverse

Kristijonas Cyras


Comparison

I ABA+ generalizes PAFs [Amgoud and Vesic, 2014]

I p ABA [Wakaki, 2014] does not generate new extensions

I ASPIC+ [Modgil and Prakken, 2014]:I contraries vs. contradictories, c-classicality,

contrapositionI different if no contrapositionI . . . in between . . .I conjecture: instance if flat, contraposition, with elitist

Kristijonas Cyras


ABA+ So Far

ABA with 6 over assumptions:reverses attacks by incorporating < directly into .

I conservative extension of ABA

I conflict preservation

I preference handling properties

I rationality postulates [Caminada and Amgoud, 2007]

I Fundamental Lemma holds with a weaker form ofcontraposition

Kristijonas Cyras


Ongoing Work

I Relaxing contrapositionI Further comparison

I contraposition: flat ABA+ as an instance ofASPIC+ with the elitist comparison ?

I likewise for Deductive Argumentation[Besnard and Hunter, 2014] ?

I map to PAFs with arguments as sets of assumptions

Kristijonas Cyras


References I

Amgoud, L. and Cayrol, C. (2002). A Reasoning Model Based on the Production of Acceptable Arguments.

Ann. Math. Artif. Intell., 34(1-3):197–215.

Amgoud, L., Cayrol, C., and Lagasquie-Schiex, M.-C. (2004). On the Bipolarity in Argumentation

Frameworks. In Delgrande, J. and Schaub, T., editors, NMR, pages 1–9, Whistler.

Amgoud, L. and Vesic, S. (2011). A New Approach for Preference-Based Argumentation Frameworks. Ann.

Math. Artif. Intell., 63(2):149–183.

Amgoud, L. and Vesic, S. (2014). Rich Preference-Based Argumentation Frameworks. Int. J. Approx.

Reasoning, 55(2):585–606.

Baroni, P., Cerutti, F., Giacomin, M., and Guida, G. (2011). AFRA: Argumentation Framework with

Recursive Attacks. Int. J. Approx. Reasoning, 52(1):19–37.

Bench-Capon, T. J. M. (2003). Persuasion in Practical Argument Using Value Based Argumentation

Frameworks. J. Log. Comput., 13(3):429–448.

Besnard, P. and Hunter, A. (2014). Constructing Argument Graphs with Deductive Arguments: A Tutorial.

Arg.&Comp., 5(1):5–30.

Bondarenko, A., Dung, P. M., Kowalski, R., and Toni, F. (1997). An Abstract, Argumentation-Theoretic

Approach to Default Reasoning. Artif. Intell., 93(97):63–101.

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References II

Booth, R., Kaci, S., and Rienstra, T. (2013). Property-Based Preferences in Abstract Argumentation. In

Perny, P., Pirlot, M., and Tsoukias, A., editors, ADT, volume 8176 of Lecture Notes in Computer Science,pages 83–100, Brussels. Springer.

Brewka, G. and Woltran, S. (2010). Abstract Dialectical Frameworks. In Lin, F., Sattler, U., and

Truszczynski, M., editors, KR, Toronto. AAAI Press.

Caminada, M. and Amgoud, L. (2007). On the Evaluation of Argumentation Formalisms. Artif. Intell.,

171(5-6):286–310.

Cyras, K. and Toni, F. (2016a). ABA+: Assumption-Based Argumentation with Preferences. In Baral, C.,

Delgrande, J. P., and Wolter, F., editors, KR, pages 553–556, Cape Town. AAAI Press.

Cyras, K. and Toni, F. (2016b). Properties of ABA+ for Non-Monotonic Reasoning. In NMR, pages 25–34,

Cape Town.

Dung, P. M., Kowalski, R., and Toni, F. (2009). Assumption-Based Argumentation. In Simari, G. R. and

Rahwan, I., editors, Argumentation Artif. Intell., pages 199–218. Springer.

Dunne, P. E., Hunter, A., McBurney, P., Parsons, S., and Wooldridge, M. (2011). Weighted Argument

Systems: Basic Definitions, Algorithms, and Complexity Results. Artif. Intell., 175(2):457–486.

Kristijonas Cyras


References III

Garcıa, A. J. and Simari, G. R. (2014). Defeasible Logic Programming: DeLP-servers, Contextual Queries,

and Explanations for Answers. Arg.&Comp., 5(1):63–88.

Kaci, S. and van der Torre, L. (2008). Preference-Based Argumentation: Arguments Supporting Multiple

Values. Int. J. Approx. Reasoning, 48(3):730–751.

Kowalski, R. and Toni, F. (1996). Abstract Argumentation. Artif. Intell. Law, 4(3-4):275–296.

Modgil, S. (2009). Reasoning About Preferences in Argumentation Frameworks. Artif. Intell.,

173(9-10):901–934.

Modgil, S. and Prakken, H. (2013). A General Account of Argumentation with Preferences. Artif. Intell.,

195:361–397.

Modgil, S. and Prakken, H. (2014). The ASPIC+ Framework for Structured Argumentation: A Tutorial.

Arg.&Comp., 5(1):31–62.

Prakken, H. and Sartor, G. (1999). A System for Defeasible Argumentation, with Defeasible Priorities. In

Wooldridge, M. and Veloso, M., editors, Artif. Intell. Today, volume 1600 of Lecture Notes in ComputerScience, pages 365–379. Springer.

Thang, P. M. and Luong, H. T. (2014). Translating Preferred Subtheories into Structured Argumentation.

J. Log. Comput., 24(4):831–850.

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References IV

Toni, F. (2014). A Tutorial on Assumption-Based Argumentation. Arg.&Comp., 5(1):89–117.

Villata, S., Boella, G., Gabbay, D. M., and van der Torre, L. (2012). Modelling Defeasible and Prioritized

Support in Bipolar Argumentation. Ann. Math. Artif. Intell., 66(1):163–197.

Wakaki, T. (2014). Assumption-Based Argumentation Equipped with Preferences. In Dam, H. K., Pitt,

J. V., Xu, Y., Governatori, G., and Ito, T., editors, PRIMA, volume 8861 of Lecture Notes in ComputerScience, pages 116–132, Gold Coast. Springer.

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